Title Page
ABSTRACT
Contents
ABBREVIATIONS 15
NOMENCLATURES 16
Chapter 1. Introduction 19
1.1. Background 19
1.2. Room Impulse response 20
1.2.1. Measurement of Room Impulse Response 20
1.2.2. Characteristic of RIR 21
1.3. RT Estimation Methods 24
1.3.1. Geometric based method 24
1.3.2. The interrupted noise method 25
1.3.3. Integrated impulse response method 27
1.3.4. Other envelope smoothing methods 28
1.4. Noise effects on the RT 29
1.4.1. Dynamic range definition 29
1.4.2. RIR characteristics on EDC 30
1.5. Motivation and Goal 32
1.5.1. Mathematical algorithms on RT estimation 32
1.5.2. Advanced Techniques 34
1.6. Structure of the Thesis 35
Chapter 2. Theory and methods 38
2.1. Noise subtraction 38
2.2. Noise truncation methods 40
2.2.1. Truncation time determination 40
2.2.2. Noise Truncation and Correction method 42
2.2.3. Noise subtraction, truncation and correction 43
2.3. Nonlinear regression method 45
2.3.1. Method based on the Schroeder decay function 45
2.3.2. Method based on the energy-time function 47
2.4. Combination of nonlinear regression method and noise compensation method 50
2.5. Conclusion 53
Chapter 3. Truncation time determination in noisy RIR 56
3.1. Procedure for detection of the TT 57
3.1.1. Influence of the decay range on TT determination 57
3.1.2. Existing iterative procedure for TT detection 58
3.2. Proposed procedure for TT detection 61
3.3. Implementation and experimentation 64
3.3.1. Experiments design 65
3.3.2. Hardware Setting 66
3.3.3. Experimental procedure 67
3.4. Analysis of the Proposed procedure 69
3.4.1. Procedure of the method 69
3.4.2. Example of parameters estimation by the procedure 71
3.5. Comparison with Proposed procedure from existing iterative procedure 73
3.5.1. TT detection for RIRs with added noise 73
3.5.2. TT detection for measured RIRs with natural ambient noise 77
3.6. Conclusions 81
Chapter 4. De-noising RIR with generalized spectral subtraction 83
4.1. Overview of principle of Spectral Subtraction 84
4.1.1. Basic Principle of Spectral Subtraction 84
4.1.2. Drawbacks of the SS 86
4.1.3. Spectral Subtraction using over-subtraction 87
4.1.4. Generalized Spectral Subtraction 89
4.2. Noise subtraction procedure for RIR 92
4.2.1. Application of the RIRs 92
4.2.2. Noise Subtraction Procedure for RIR 93
4.3. Results analysis and discussion 96
4.3.1. Performance of the GBSS algorithm factors 96
4.3.2. Performance of the Optimal factors 100
4.4. Over-subtraction factor for the octave band RIRs and different noises 103
4.5. GBSS method in measured RIRs with natural ambient noise 109
4.6. Conclusions 113
Chapter 5. Conclusion 114
References 118
Table 1. Information about the measured rooms. 65
Table 2. Comparison of DT and TTs between the measured RIRs with added pink noise 74
Table 3. Comparison of DTs between the measured RIRs with two noise levels 79
Table 3. Comparison of RTs and EDT between the de-noised RIRs and the reference RIRs. 106
Table 4. Comparison of RTs and EDT between the de-noised RIRs and the compensated RIRs 111
Figure 1.1. An acoustical impulse response consists of sound from an excitation source arriving at a measurement position by multiple pathways, both direct and reflected. 20
Figure 1.2. Principle of room impulse response measurement. 22
Figure 1.3. An example of the impulse response with its main components: direct sound, early reflection, and late reverberation. 22
Figure 1.4. The generation of reverberant speech. 23
Figure 1.5. An example of the RT derived from the decay curve corresponding to the energy time curve (ETC). 26
Figure 1.6. An example of the RT derived from the decay curve corresponding to the energy decay curve (EDC). 28
Figure 1.7. Flowchart of current procedure in RT estimated from the EDC in octave-band or one-third octave band. 31
Figure 1.8. The decay slope derived from the EDC follows the estimated decay range of the ETC filtered in 1000Hz. (a) Normalized ETC of a measured RIR synthesized with pink noise: allowing... 31
Figure 2.1. Example of the RIR (a) and corresponding EDCs (b) with subtraction of the estimated noise levels. The influence of the noise on EDC is minimized, but the dynamic range... 39
Figure 2.2. Example of the RIR (a) and corresponding EDCs (b) with truncating the RIR at different TTs (TT, TT1 and TT2). The influence of the noise on EDC and the extended dynamic... 41
Figure 2.3. Example of the RIR (a) and corresponding EDCs (b) with truncating the RIR and correction term for the truncation at TT. The influence of the truncation error at the TT is reduced... 43
Figure 2.4. Example of the RIR (a) and corresponding EDCs (b) with subtraction the noise, truncating the RIR and correction term for the truncation at TT. The noise effects on the EDC are... 44
Figure 2.5. Example of the Schroeder decay model along with single exponential decay slope and linear noise decay term fitted to the measured RIR illustrated in logarithmic in dB scale. 46
Figure 2.6. Comparison of parameters derived from the logarithmic decay model (blue dotted line) and noise compensation method presented in Chapter 2.2.2: (a) Decay curves of the measured RIR... 49
Figure 2.7. Effects of changing the estimation range of the RIR on the logarithmic decay curves (blue line) and Schroeder decay curve (blue dotted line) together with the corresponding TT as... 52
Figure 2.8. The existing methods presented in this Chapter deriving the decay slope and RT. 54
Figure 3.1. Flowchart of the iterative procedure. 56
Figure 3.2. Detection of TT to be dependent on the ER: (a) The preliminary TT generated from the estimated ER. (b) The final TT generates from the ER with a selection slope margin and noise margin. 58
Figure 3.3. Truncated EDCs and corresponding TT generated from the noise compensation method: (a) Reference EDC and the truncated EDCs results from the noise compensation method... 60
Figure 3.4. Logarithmic decay curves (black dotted line) and Schroeder decay curve (blue dotted line) generated from the model (Eq.31) after applying LS optimization together with the... 62
Figure 3.5. RIR with different noise levels measured in three rooms: (a) Anechoic chamber, (b) Room A, and (c) Classroom A, (d) Classroom B, and (e) Hall. 66
Figure 3.6. Hardware set-up 67
Figure 3.7. Comparison of the reference EDC and the EDC obtained from the model given in Eq.40 and corresponding TT₁ and TT₂ estimated in Eq.6 by implementing the proposed procedure... 72
Figure 3.8. Comparison of the normalized EDCs generated from the proposed procedure with the non-exponential decay model (Eq.40) and the measured RIR with added pink noise (-60dB to -... 74
Figure 3.9. Comparison of the results of the proposed procedure and the reference method with added pink noise (-60dB to -40dB) and band-pass filtering at the 1kHz and 500Hz: (a) and (b) The... 76
Figure 3.10. Comparison of normalized EDCs generated from the proposed procedure with the non-exponential decay model (Eq.7) and two measured RIRs having non-exponential decays... 78
Figure 3.11. Comparison of the proposed procedure and the compensation method for the RIR measured with ambient noise in two rooms and filtered in octave bands: (a) and (b) Comparison of... 80
Figure 4.1. General form of the spectrum subtraction algorithm. 85
Figure 4.2. An example power spectrum of the enhanced signal after half-wave rectification in subtraction process. (a) Noisy signal with the noise power spectrum (dotted line) (b) enhanced... 87
Figure 4.3. Application of SS with and without VAD. (a) De-noised RIR. (b) EDC corresponding to the de-noised RIR. 88
Figure 4.4. General form of the GBSS algorithm. 90
Figure 4.5. An example power spectrum of the enhanced signal after GBSS with various ß and α. (a) Noisy signal with the noise power spectrum (dotted line) (b) effects of the enhanced power... 91
Figure 4.6. Dynamic range improvement of the EDC between the cross-point A at a noisy RIR and the cross-point B at RIR after the GBSS. 95
Figure 4.7. Comparison of the noisy RIRs and de-noised RIR at 1kHz of varying the noise spectral floor ß for a fixed value of α₀. (a) The EDCs of the RIRs (b) Power spectrum of the RIRs... 98
Figure 4.8. Comparison of the noisy RIRs and de-noised RIR at 1kHz of varying the noise over subtraction α₀ for a fixed value of ß. (a), (b) Generated EDCs of the RIRs. (c), (d) De-RIRs with... 99
Figure 4.9. De-noising effects at the knee with various factors α₀. (a) Comparison of the dynamic range at the cross point. (b), (c), (d) Comparison of the de-noised RIRs to the reference RIRs at... 102
Figure 4.10. De-noising effects using the optimal sets factors of the GBSS on the RIRs of the meeting room with different added noises filtered at the octave bands. The red dotted line is the... 104
Figure 4.11. Comparison of the RTs of the filtered RIRs at octave bands with pink noise and white noise have noise levels -60dB and -50dB. 105
Figure 4.12. Results of the optimal α₀ for different SNRs of three filtered RIRs at octave bands with two types of noise and various noise levels (-65dB to -40dB estimated in broadband RIRs)... 108
Figure 4.13. Effects of the GBSS algorithm and compensation method to the measured RIRs filtered in octave bands (250Hz and 2kHz): (a) and (b) comparison results for room A; (c) and (d)... 111
Figure 4.14. Comparison of the GBSS algorithm and the Compensation method. (a) Reverberation time relative errors. (b) Early decay time relative errors. 112